Orderable 3-manifold groups
Abstract
We investigate the orderability properties of fundamental groups of 3-dimensional manifolds. Many 3-manifold groups support left-invariant orderings, including all compact P^2-irreducible manifolds with positive first Betti number. For seven of the eight geometries (excluding hyperbolic) we are able to characterize which manifolds' groups support a left-invariant or bi-invariant ordering. We also show that manifolds modelled on these geometries have virtually bi-orderable groups. The question of virtual orderability of 3-manifold groups in general, and even hyperbolic manifolds, remains open, and is closely related to conjectures of Waldhausen and others.
Cite
@article{arxiv.math/0211110,
title = {Orderable 3-manifold groups},
author = {Steven Boyer and Dale Rolfsen and Bert Wiest},
journal= {arXiv preprint arXiv:math/0211110},
year = {2007}
}
Comments
37 pages. Published version. Improvements in the organisation and presentation of the material